An Alternative to Dark Matter and Dark Energy: Scale-Dependent Gravity in Superfluid Vacuum Theory

Abstract

We derive an effective gravitational potential, induced by the quantum wavefunction of a physical vacuum of a self-gravitating configuration, while the vacuum itself is viewed as the superfluid described by the logarithmic quantum wave equation. We determine that gravity has a multiple-scale pattern, to such an extent that one can distinguish sub-Newtonian, Newtonian, galactic, extragalactic and cosmological terms. The last of these dominates at the largest length scale of the model, where superfluid vacuum induces an asymptotically Friedmann–Lemaître–Robertson–Walker-type spacetime, which provides an explanation for the accelerating expansion of the Universe. The model describes different types of expansion mechanisms, which could explain the discrepancy between measurements of the Hubble constant using different methods. On a galactic scale, our model explains the non-Keplerian behaviour of galactic rotation curves, and also why their profiles can vary depending on the galaxy. It also makes a number of predictions about the behaviour of gravity at larger galactic and extragalactic scales. We demonstrate how the behaviour of rotation curves varies with distance from a gravitating center, growing from an inner galactic scale towards a metagalactic scale: A squared orbital velocity’s profile crosses over from Keplerian to flat, and then to non-flat. The asymptotic non-flat regime is thus expected to be seen in the outer regions of large spiral galaxies.

On asymptotic behaviour of galactic rotation curves in superfluid vacuum theory

“…One of these theories is logarithmic superfluid vacuum theory, whose foundations can be found in [5,6]. To the best of our knowledge, this model is not only free from the abovementioned limitations, but also explains the known DMand DE-attributed phenomena, and predicts a number of new effects, including vacuum Cherenkov radiation, deformed dispersion relations, mass generation and superfluid stars [7][8][9][10][11][12]. More relevant to the purposes of this paper, works [6,11] describe a number of astronomicalscale effects predicted by logarithmic SVT; including various expansion mechanisms and non-Keplerian (flat followed by non-flat) behaviour of galactic rotation curves.…”

“…When applying them to the theory of physical vacuum, one can show that this background superfluid induces a four-dimensional spacetime, while photon-like excitations are somewhat analogous to acoustic waves in laboratory superfluids, traveling at the speed c b = b 0 /m in the ap-proximation of a homogeneous isothermal liquid [6,11]. In the "phononic" (low-momentum) limit, c → c (0) ≈ c where c = 2.998 × 10 5 km/s is called, for historical reasons, the speed of light in vacuum.…”

“…For our purposes here, we assume spherical symmetry, and omit terms which decay faster than an inverse distance at spatial infinity, in which case the induced metric can be written in static coordinates in the form [11]:…”

“…The second group are parameters a's and χ of a trial wavefunction of the state |Ψ vac our superfluid is in, which is defined as a solution of a logarithmic quantum wave equation, further details can be found in section 3 of [11]. We expect that this state is stable, or at least metastable, with a sufficiently large lifetime; therefore it is thus natural to assume that it is a ground state, or close to, stationary and rotationally invariant.…”

Editorial to the Special Issue “Selected Papers from the 17th Russian Gravitational Conference—International Conference on Gravitation, Cosmology and Astrophysics (RUSGRAV-17)”

“…Among them one could mention the problems of dark matter and dark energy, as well as a failure of all attempts to create consistent quantum theory of gravity based on general relativity theory. Scale-dependent gravity in the superfluid vacuum theory is considered in [26] as a possible alternative to dark matter and dark energy. Three articles are devoted to quark stars in massive Brans-Dicke gravity with Tolman-Kuchowicz spacetime [27], non-relativistic limit of embedding gravity as general relativity with dark matter [28], and to the formation and clustering of primordial black holes in Brans-Dicke theory [29].…”